The John Pickstock you refer to may be the son of James b1817, Samuel b1819 or Thomas b1823. These are the eldest three of twelve children born to Thomas Pickstock 1792 - 1864 and Maria Reade 1800 - 1870. The birth years of the other four male children make it unlikely that your John was born to any of them. I am certain that all twelve children were born in Over.
If the John you seek is not in this line Thomas 1792 -1864 had four male siblings, Samuel, Job, James and Daniel who were born in Great Budworth, Cheshire. A search of the Parish records there may pay dividends.